I agree with the semi-colon addition because there are two statements being made: "The adaptation was farming; the global-warming crisis that gave rise to it happened more than 10,000 years ago." I don't know how you analyze this sentence, but I noted the following: The first independent clause is rather simple: "the adaptation was farming." It's two nouns linked by a copula, "was", which is the past tense of "to be" verb. "Farming" is a gerund - a noun created from a verb. For the second sentence, the simple subject is "crisis" and the simple predicated is "happened". The "global-warming" compound adjective modifies subject; similarly, "that gave rise to it" is the prepositional phrase that modifies "crisis". These are all modifiers, because you can simply take it out and the sentence still makes sense, just with less details: "The crisis happened more than 10,000 years ago." Similarly, "more than 10,000 years ago" modifies the predicate, "happened". If you pull this modifier out, the sentence also makes sense although it does not tell you much: "The crisis happened."

There are 2 statements in this sentence, with the second statement qualifying the first. I suggest that the only punctuation needed is a semi-colon: "The adaptation was farming; the global-warming crisis that gave rise to it happened more than 10,000 years ago" The 'global warming' that occured more than 10,000 years ago was the end of the last ice-age; it might be better to call this an 'event', rather than a 'crisis'.

First, that's a weird sentence :P I can't even analyze it. Second, when you want to analyze the grammatical elements, look for the verb first. Is it an action verb or be-verb? That always seems to help.